In the discussion of global warming, the time it takes for a process to double is often one of the key issues, and has come up a couple of times in the comments thread. There’s a neat rule on this which I thought was worth a short post. For moderate growth rates, you can get the doubling time just by dividing the percentage growth rate into 70. That is, an economy with a 1 per cent growth rate doubles its output in 70 years, 2 per cent takes 35 years and so on.

The key to this rule is the fact that the natural log of 2 is just about 0.7. Actually it’s 0.693, but 69 doesn’t have as many prime factors and ‘The Rule of 69’ is hard to say with a straight face.

Jeff Madrick observes that unemployment pinches hard at the bottom of the economic ladder. As he observes the steady growth in US inequality observed over recent decades was briefly reversed, or at least halted, in the late 1990s when the unemployment rate fell to 4 per cent. Beginning in 2000, the growth in inequality has resumed.

Maddrick concludes correctly that the rate of unemployment is a major factor in driving the growth in inequality. But he is over-optimistic in saying that the experience of the 1990s proves that unemployment can be pushed down to 4 per cent and kept there. The late 1990s represented an unsustainable and probably unrepeatable bubble. At least under its current economic institutions, the US can’t hold unemployment much below 6 per cent. It follows that the same institutions generate steadily increasing inequality.

Of course, other countries haven’t done notably better on unemployment. Allowing for distorting factors like disability benefits, and differing propensities to imprison the unemployable, there isn’t a lot of difference between US, European, Australian and Japanese unemployment rates. But at current unemployment rates the US, and other English speaking countries have seen a lot of growth in (already high) inequality, whereas inequality in Europe and Japan has been much lower and fairly stable.

Ken Parish responds to my piece on the rate of global warming with a range of issues. I’ll start with the easy ones. Ken notes what appear to be two offsetting errors, saying

[John] says the current warming record shows a trend of 0.2 degrees C per decade. In fact, it’s about 0.4 degrees over the last 26 years (which is somewhat lower than John says). John also observes that IPCC says about half of this increase is attributable to human emissions of greenhouse gases. In fact IPCC says just under 3/4 is attributable to human emissions. As you can see, this amounts to approximately 0.1 degrees C per decade from human greenhouse emissions. Hence, as I’ve observed before, a straight line extrapolation of current warming trends results in an approximate temperature increase of about 1 degree C by 2100. John reaches that figure (because his two errors cancel each other out), and agrees that a warming of that magnitude and speed isn’t too much to worry about.

I’ve been a bit rushed during the move, and have been making a few minor errors, but this time I’m pretty much in the clear. I ran a regression estimate for the trend which came out at 0.196 degrees per decade and I knew that the IPCC had attributed 0.1 degrees to emissions so I worked backward to get 1/2.

Ken also makes some good points about population growth, saying that UN estimates have been revised downwards. However, the most contentious IPCC estimates (the A scenarios) have population stabilising around 9 billion, which is the estimate cited by Ken.
The big issue relates to the question of whether if economic growth continues at , say, 3.6 per cent per year, and no specific mitigation action is taken, emissions will keep growing or remain stable. I assert that, under Business As Usual emissions are likely to double. Ken suggests that this requires that the rate of economic growth should also double to 7.2 per cent. I say that as long as GDP grows steadily at a constant rate, so will emissions and therefore the rate of growth of atmospheric concentration and the rate of increase of equilibrium temperature.

Ken’s argument reflects a confusion between stocks, flows and acceleration. HTML is not well-suited to resolving this kind of thing, but I’ll try my best. Under the standard model in which equilbrium temperature depends on the concentration of greenhouse gases, the following types of variables should move together (not necessarily proportionally, since there are lags, sinks, feedbacks etc)

Stocks
Concentration of CO2
Equilibrium Temperature
Cumulative Emissions
Cumulative world output of goods &services

Flows
Addition to concentrations of CO2
Rate of change in equilibrium temperature
Annual emissions
Annual output (GDP)

Accelerations
Acceleration in growth of CO2 concentration
Acceleration in temperature change
Rate of growth of annual emissions
Rate of growth of GDP

So with a constant growth rate of GDP (and BAU) , output, emissions and the rate of temperature change all rise steadily. Because the energy-intensity of GDP declines with rising income, you need something like a quadrupling of GDP tp get a doubling of emissions, but this doesn’t affect the main point.

It’s not easy to see this by eyeballing the data for a decade or two – in fact, it’s quite difficult statistically to distinguish between a linear trend and an exponential if the growth rate is modest. But the basic logic set out above is clear-cut. I’ll try soon to make available a PDF file in which this is proved algebraically – words are really cumbersome for this kind of problem.

Chris Suellentrop at Slate does a job on Hans Blix, the head of the UNMOVIC, the UN weapons inspection team. Unlike most of the many critics of Blix, he does concede Blix’s role in detecting the North Korean nuclear program. But as with the majority of US commentary on this issue, he fails to mention the fact that the first set of UN inspections found and destroyed Saddam’s nuclear weapons program.

This is not to say that Saddam may not have tried again, and of course he’s used chemical weapons (let’s pass over the fact that he was a ‘good guy’ at the time). But the assumption that inspections are bound to fail seems misplaced to me, especially as the Iraqis are taking a strong line in denial, rather than making some sort of ambiguous half-admission. If they haven’t destroyed (nearly) everything it shouldn’t be too hard to catch them.

Of course there could be data on a CD-ROM in Saddam’s jacket pocket, but nearly every actual weapon is detectable and the Iraqis are almost certainly behind the curve in their knowledge of advances in detection techniques over the past decade.

Don Arthur has a string of great posts, including one on whether posts should be short and sharp. I don’t think they need to be, but the problem is that it’s easier to do a short, sharp link to a short sharp post. I can’t think of anything short and sharp to say about Don’s recent thoughts, except that everyone should go and read them. The same goes for Rob Schaap.

Update As so often with this blog, the comments thread adds far more value to the debate than the original post. Read the fascinating discussion between Simon and Ken Parish, with a brief contribution from me. Then read Don Arthur and Rob Schaap. That’ll take quite a while, but I think it’s time better spent than on the opinion pages of the papers or watching the TV news.

Meanwhile my open forum (Thoughts for Thursday) is uncharacteristically quiet. There seem to be lots of new visitors to the blog since I completed my move to Queensland, so why don’t you share your thoughts on any topic you please, particularly what you like or don’t like about this blog.

Now that I’m back in sunny Queensland I need a sunshield for the windscreen of my car. So I dragged out the one I bought when I lived in the US ten years ago. On the back, along with the patent numbers etc, it bears the warning DO NOT DRIVE WITH SHIELD IN PLACE

I wonder, did someone actually do this and sue them, or do consumer products companies have staff paid to think of really dumb ways their customers could injure themselves.

Bruce Wolpe has an interesting comparison of Australian and American responses to terrorist attacks, noting that Australia is a place where the pursuit of happiness is taken seriously. I mentioned a while ago that Australia could do with our own version of the First Amendment. If we ever become a republic, it would be nice if we could manage a founding document that could bear comparison with the Declaration of Independence.

Monday messages have been very successful, but people tend to stop commenting once the post falls halfway down the page. So I’ve decided to go bi-weekly with this feature. You can post your thoughts on any topic in the comments thread for this post (civilised discussion and no coarse language).

My suggested starter – what can I do to improve this blog? Suggestions that I should get someone else to write it will not be entertained.

I’m making painstaking progress with transferring my website to UQ. Here’s the promised review of Lessig.

An interesting sidelight is that my ANU website had absolute addresses (that is, the complete URL) whereas the orthodoxy says you should have relative addresses to make transfers easy. The positive result is that having copied my homepage to the UQ site, all the links to files at ANU still work. I’m not sure if this refutes the standard argument for relative addresses, but it certainly tips the balance a bit.

A great piece from the unsilenceable Salman Rushdie. Just above it on the NYT Op-Ed page, Thomas Friedman’s piece on similar lines isn’t bad, but looks tired by comparison.